Eōdem tempore Tarentīnīs, quī iam in ultimā Italiā sunt, bellum indictum est, quia lēgātīs Rōmānōrum iniūriam fēcissent.
War was at the same time proclaimed against the Tarentines, who are still a people at the extremity of Italy, because they had offered violence to some Roman ambassadors.
Why is fēcissent in the subjunctive?
This is a subjunctive of quoted reason, I believe; in this case the reason is given as that of the Romans.
Subjunctive of Quoted Reason: Just as dependent clauses in indirect statement take subjunctive verbs, so causal conjunctions such as quod, quia, quoniam will take subjunctive verbs when the speaker is indicating that he/she is stating someone else’s reason; e.g., Pliny Ep. 4.19: …quod me sibi dederis: [my wife thanks you] because you gave me to her.
http://www2.iona.edu/faculty/latin/syntax2.html
Probably also known under another name since I had trouble finding this.
If I’m wrong I’ll stop answering questions again.
I would translate jam to indicate emphasis, rather than time. See II-C in Lewis & Short